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Proof step 63 from proof refine-add-gnds (previous step)

elems nx0 ∩ ginval0 = ∅, dom gstore2 ∪ elems nx0 = dom gstore ∪ ginval0, remove-refsize0(gstore2) = gstore2, remove-refsize0(istore0) = istore0, gstore[maxino] = groupblock(gndlist0, lax0, m, m0, m1, false), gstore1 = gstore[maxino, groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, m, LEB_SIZE, m1, true)], gstore0 = gstore[maxino, groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, m, LEB_SIZE, m1, true)], # lax1 ≠ # gndlist, gndlist ≠ [], maxino ∈ gstore, inv-flashsize(prefixn(# lax1, gndlist), lax1), # lax1 < # gndlist, m0 + gndlist.flashsize ≤ LEB_SIZE, btree-inv(rp, adr, gstore \ ginval0, istore, istore0, zh, fi, fi0, ld), inv(gstore \ ginval0), inv(gstore2), flushed(gstore \ (ginval0 ∪ elems nx0)), ri-inj(fi), ri-inj(fi0), btree-inv(rp, adr, gstore \ ginval0, istore, istore0, zh, ri, fi1, ld0), inv(istore), inv(istore0), flushed(istore0), istore0 ⊑ istore, btree-inv(rp, adr, gstore \ ginval0, istore, istore0, zh, ri0, fi2, ld1), maxino ∈ nx0, inv(groupblock(gndlist0, lax0, m, m0, m1, false)), ⌊err1⌋ , gstore2 \ ginval0 lpt= gstore \ elems nx0, flushed(gstore[maxino, groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, n, LEB_SIZE, m1, true)] \ (ginval0 ∪ elems nx0)), inv(groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, n, LEB_SIZE, m1, true)), btree-inv (rp, adr, gstore[maxino, groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, n, LEB_SIZE, m1, true)] \ ginval0, istore, istore0, zh, ri1, fi3, ld2), n ≤ # gndlist0 + # lax1, m ≤ n, m ≤ # gndlist0 + # lax1, ¬ dups(lax1), ¬ dups(nx0), ¬ maxino ∈ ginval0, gstore0[maxino] = groupblock(gndlist1, lax, m2, m3, m4, boolvar) ⊦ ∃ ax. ⟨choose n with m2 ≤ n ∧ n ≤ # gndlist1 in gstore0[maxino].flushindex := n⟩ ( gstore0 = gstore1[maxino, gstore1[maxino].flushindex:= n] ∧ btree-inv(rp, adr, gstore1[maxino, gstore1[maxino].flushindex:= n] \ ginval0, istore, istore0, zh, fi, fi0, ld) ∧ ax2 = ax)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 64:
gndlist0 + prefixn(# lax1, gndlist) = gndlist1, gstore1 = gstore[maxino, groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, m2, LEB_SIZE, m1, true)], gstore[maxino] = groupblock(gndlist0, lax0, m2, m0, m1, false), remove-refsize0(istore0) = istore0, remove-refsize0(gstore2) = gstore2, dom gstore2 ∪ elems nx0 = dom gstore ∪ ginval0, elems nx0 ∩ ginval0 = ∅, gstore0 = gstore[maxino, groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, m2, LEB_SIZE, m1, true)], gndlist ≠ [], # lax1 ≠ # gndlist, m2 ≤ n, n ≤ # gndlist0 + # lax1, btree-inv (rp, adr, gstore[maxino, groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, n, LEB_SIZE, m1, true)] \ ginval0, istore, istore0, zh, ri1, fi3, ld2), inv(groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, n, LEB_SIZE, m1, true)), flushed(gstore[maxino, groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, n, LEB_SIZE, m1, true)] \ (ginval0 ∪ elems nx0)), gstore2 \ ginval0 lpt= gstore \ elems nx0, ⌊err1⌋ , maxino ∈ nx0, btree-inv(rp, adr, gstore \ ginval0, istore, istore0, zh, ri0, fi2, ld1), istore0 ⊑ istore, flushed(istore0), inv(istore0), inv(istore), btree-inv(rp, adr, gstore \ ginval0, istore, istore0, zh, ri, fi1, ld0), ri-inj(fi0), ri-inj(fi), flushed(gstore \ (ginval0 ∪ elems nx0)), inv(gstore2), inv(gstore \ ginval0), btree-inv(rp, adr, gstore \ ginval0, istore, istore0, zh, fi, fi0, ld), m0 + gndlist.flashsize ≤ LEB_SIZE, # lax1 < # gndlist, inv-flashsize(prefixn(# lax1, gndlist), lax1), maxino ∈ gstore, m2 ≤ # gndlist0 + # lax1, inv(groupblock(gndlist0, lax0, m2, m0, m1, false)), ¬ maxino ∈ ginval0, ¬ dups(nx0), ¬ dups(lax1) ⊦ ∃ ax. ⟨choose n with m2 ≤ n ∧ n ≤ # gndlist1 in gstore0[maxino].flushindex := n⟩ ( gstore0 = gstore1[maxino, gstore1[maxino].flushindex:= n] ∧ btree-inv(rp, adr, gstore1[maxino, gstore1[maxino].flushindex:= n] \ ginval0, istore, istore0, zh, fi, fi0, ld) ∧ ax2 = ax)

Rule argument

Additional information

Used simplifier rules: let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%fwd-inv-gblock-rem: ⊦ inv(gstore \ ginval) ∧ n ∈ gstore ∧ ¬ n ∈ ginval ∧ gstore[n] = gblock → inv(gblock); (forward) from specification apersistence-base%inj: ⊦ groupblock(gndlist, lax, m, m0, m1, boolvar) = groupblock(gndlist0, lax0, m2, m3, m4, boolvar0) ↔ gndlist = gndlist0 ∧ lax = lax0 ∧ m = m2 ∧ m0 = m3 ∧ m1 = m4 ∧ (boolvar ↔ boolvar0); from specification ablock[group-store]%At-same: ⊦ gstore[n, gblock][n] = gblock; from specification store[group-store-ablock-store-nat-store]